Find x, y if \left[\begin{array}{cc}-2 & 0 \ 3 & 1 ]\end{array}\left[\begin{array}{c}-1 \ 2 x ]\end{array}+3\left[\begin{array}{c}-2 \ 1 ]\end{array} =2\left[\begin{array}{c}y \ 3 ]\end{array} \text{. }

ICSE Class X Math 2014 Solved Paper - Question 6

Question : 6 of 52

Marks: +1, -0

Find

x, y

{[\table -2 , 0 ; 3 , 1 ]}{[\table -1 ; 2 x ]}+3{[\table -2 ; 1 ]}

=2{[\table y ; 3 ]} \;\text ". "\;

Solution:

Given

{{[\table -2 , 0 ; 3 , 1 ]}{[\table -1 ; 2 x ]}+3{[\table -2 ; 1 ]} }\;

=2{[\table y ; 3 ]}

{{[\table -2 ×-1+0 × 2 x ; 3 ×-1+1 × 2 x ]}+{[\table -6 ; 3 ]} }\;

={[\table 2 y ; 6 ]}

{{[\table 2 ; -3+2 x ]}+{[\table -6 ; 3 ]} }\;

={[\table 2 y ; 6 ]}

{{[\table 2-6 ; -3+2 x+3 ]} }\;={[\table 2 y ; 6 ]}

{{[\table -4 ; 2 x ]} }\;={[\table 2 y ; 6 ]}

Comparing the cofficiant

\;2 y\;=-4 \;\text " and "\; 2 x=6

⇒ y\;=-2 \;\text " and "\; x=3

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